Volume 112B, number 2 PHYSICS LETTERS 6 May 1982

ON THE 180 POSITIVE-PARITY ROTATIONAL BAND

A. CUNSOLO, A. FOTI, G. IMMI~, G. PAPPALARDO, G. RACITI Istituto Nazionale di Fisica Nucleare, Sezzone dl Catania, Centro Sictliano dz Flsica Nucleare e dl Struttura della Materta, Istituto di Fiswa dell 'Universitd di Catama, 95129 Catama, Italy

and

N. SAUNIER Ddpartement de Physique ,Vucldaire, Centre d'Etude Nucl~alre de Saclay, 91190 Gif sur Yvette, France

Received 11 February 1982

Deuteron--alpha angular correlations have been measured for the reaction 14C(6Li, d)l So* ~ a o + 14C at E(6LI) = 34 MeV and 0d hb = 10 ° Transitions revolving the 11 69 MeV (6+) and the 17.6 ± 0.2 MeV 180 states have been analyzed Spin and panty are confirmed for the known 11 69 MeV (6 ÷) state and assigned to be 8 + for the 17 6 MeV level. This last is suggested to be the fifth member of the positive-parity 180 rotanonal band built on the 3.63 McV (0 ÷) level.

In a recent paper [ 1 ] , hereafter referred as 1, we published an investigation of the 14C(6Li, d)180 reac- tion at 34 MeV incident energy. It was found that, for the strongest transitions, the reaction mainly proceeds through direct a-transfer, and a-spectroscopic strengths for 180 states up to 17 MeV excitation en- ergy were extracted. In particular evidence was found corroborating the existence of a positive-parity 180 rotational band based on the 0~ state at 3.63 MeV, with the 2 + member at 5.26 MeV, the 4 + at 7.11 MeV and the 6 + at 11.69 MeV.

Theoretically, as these states have been described as 14C ® 4He cluster states with strond (sd)4(p) - 2

components , the highest spin member should be a j , r = 8 + state.

In fact Buck et al. [2] , in the framework of the a- cluster folding model [3] , have calculated E x = 18.03 MeV for this 8 + state. Extrapolat ion based on the J ( J

+ 1 ) rule gives roughly the same excitation energy E x = 17.0 +- 0.9 MeV.

Experimental ly, the 8 + state is, up to now, un- known. However, as shown in fig. la , on the strong taft of the continuous deuteron spectrum, a weak peak at 17.6 -+ 0.2 MeV can be seen in the 14C(6Li, d) deu- teron spectrum.

Unfortunately even assuming that this peak is due to the excitation of only one state, the structureless angular distribution, obtained through a new analysis of data of ref. [1], shown in fig. 2, does not allow an unambiguous spin assignment. This, however, can be done by studying the a-decay from this state, i.e. by measuring the d - a angular correlation [4]. In addi- tion, if deuterons are detected at 0d hb 4: 0, informa- tion on the (6Li, d) reaction mechanism can be ob- tained [5,6]. The d - a angular correlation experiment was performed by bombarding a 14C target 180 ~tg/ cm 2 thick and enriched to 70%, with a 34 MeV 6Li beam from the CEN Saclay FN tandem Van de Graaff.

Deuterons were detected at 0 lab = 10 ° ($d = 0° azimuthal angle) and coincident a-particles in the range 0~ ab = 2 0 ° - 1 0 7 ° (¢) = 180 ° azimuthal angle). The experimental set-up and procedure have been de- scribed in detail elsewhere [6].

In order to subtract coincidences due to the 12C target tmpurity, measurements where also performed with a natural carbon target As an example, in figs. lb and lc are shown d--a 0 coincident events proJect- ed onto the deuteron energy axis, recorded when us- ing (14C + 12C) target and the natural 12C target, re-

spectively. The angular correlation data for the 11.69

0 031-9163/82/0000-0000/$02.75 © 1982 North-Holland 121

Volume 112B, number 2 PttYSICS LETTERS 6 May 1982 12000[ 60CC~-

I- z /b

0 L)

"SL_ 0

C( LI "J) O- " Q . "C~

E ( L , ) 3Mv'ev

@,-,_ lC =

1

/ ,

-"..A a)

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" Na u '~ l C - target

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I

I78 256 384

3.- A N N L L

c)

512

l lg 1. Single and coincxdcnce spectra from the reaction 12,14C(6L1, d)16.180--, oL + 12,14Cg s at E(6I 1) = 34 MeV. (a)

^lab _ Singles deuteron spectrum measured at u d - 10 °. The energy cahbrauon was obtained from transitions leading to known 180 and 160 states [he overall energy resolution (FWHM) was about 100 keV (b) Deuteron spectrum in coincadence with cz-partlcles decaying to the 14Cground state, measured at 0 lab = 55 °. Contributions from the ~eC target impurity are also present. (c) Same as (b) but tbr the reaction 12C(6Li, d)160 --, c~ + ]2Cg s Note that in the investigated energy region, the IZC background is very small.

MeV (6 +) and 17.6 MeV 180 states are displayed in

fig. 3. The theoretical calculations, shown in fig. 3, are

based on the hypothesis of the sequential process lnC(6Li, d)180*(J 7r) ~ ot + 14 C ,s-

In tlus case the angular correlation W(~21, ~22) is proportaonal to the square of a Legendre polynomial of order J, shifted over an angle 6 that depends on the primary reaction mechanism [ 4 - 6 ] .

In particular the prtmary reaction (6Li, d) has been described as a direct a4ransfer leading to a weU-def'm- ed 180 state, with spin J and parity rr, which under- goes a-decay to the 14C ground state.

The (6Li, d) reaction has been treated in the Exact- Finite-Range-Distor ted-Wave-Born-Approxima tion (EFR--DWBA) framework. Calculations have been

I00C

500 "z" J1

IOC

) 5c

'C(~L,,d ) '~0

E(~'L, ) = 3 4 MeV

E: =17 6MeV ~0 (8 ÷)

I i I i I ,

10 30 50 70

®cm(deg )

Fig 2 Angular distribuUon of deuterons from the 14C(6Li. d)180 reaction at E(6Li) = 34 MeV leading to the 17.6 MeV 180 state I he dashed curve represents a llauscr--t eshbach calculation; the full curve represents the incoherent sum

S 8+, (do/dI~)EFR_DWB A + (do/dI2)HF

done by using the code CORRELA [7] and assuming jTr = 5 and 6 + for the 11.69 MeV level a n d J ~r = 6 +, 7--

or 8 + for that at 17.6 MeV. For the DWBA part the optical model parameters have been used of ref. [ 1 ].

As can be inferred from fig. 3, the lowest state is confirmed to have J~ = 6 +, whereas the highest state has j , r = 8 +. In fig. 3 the curve for J'~ = 7 - is not showal because it oscillates out-of-phase with respect to the data. It must be noted that the angular correla- tion curves calculated by assuming a statistical com- pound nucleus mechanism for the (6Li, d) reaction

show oscillations much less pronounced than experi- mentally observed (see e.g ref. [6]). Furthermore the agreement between experimental and theoretical angular " DWBA o shifts (811 69 = 14.4 ;8]]P69 = 13.5 -+ 0.5°; 6 D~BA = 8 o, 6 ~ . 6 = 6.5 -+ 0.5 °) corroborates the

hypothesis of an a-transfer for the primary reaction. Finally the analysis of the 17.6 MeV (8 +) angular

distribution data of fig. 2, performed in the s a m e way as in 1 and assuming for this state a 4 p - 2 h main con- figuration, gives a relative a-particle spectroscopic

122

Volume 112B. number 2 PIIYSICS LE'ITERS 6 May 1982

(!)

I [ '~C (6L , . d ) "~0"--- O..'~'C<. ~,

I E (:'LI) = 34 MeV O~ =10,> E'~ o :11 69 MeV

10- r ~ , , J":6+

[ ~,,, o . - . - ..... S : 5 -

t v i ,,l, ;,"A ", I I1,, I' i

°tll / llil 1 i / 7 I 111[ I I ' I I I

E:o=176 MeV

_ _ 7 ~ = 8 + ', ?

10 ,,\ ,4--- . . . . . J " : 6+ ,

1 20 40 6'0 8'o I~o 1½o 14o

O~ (c leg)

Fig. 3 Angular correlation functions for the 11 69 MeV and 17.6 MeV 180 states. The curves represent theoretical calcula- tions performed by assuming direct a-transfer tor the orimary reaction and different spinJ "lhe x 2 values for J= 8 andJ = 6 in the 17 6 MeV case are 15 and 30, respectively

strengthSS+/s°+2 = 0.9 + 0.2. Even if the ambiguity in the background evaluation increases the errors m the angular distribution data and henceforth in the extracted $8*/ S0~ value, we note that this value is very close to those found in I for the 6~, 4~, 2~ and 0~ states.

As shown in fig. 4, the energy of the 17.6 MeV (8 +) state is consistent with the J(J + 1) rule. All these findings lead us to indicate that the 17.6 MeV (8 +) state is the fifth member of the 4 p - 2 h !80 positive-parity rotational band.

In summary, a 8 + state of the 180 nucleus has

o

C~ w

Z i,i

Z 0

I.---

(_1

20

° : 10¸:?/ , 2 , , , ÷ , . I , I, ~, I , I , I , "~ :

0 8 16 24 32 40 48 56 64 7270-÷1)

Fig 4. Lnergies of the posmve-panty 180 slates versus J(J + 1) rhe slope of the full lane gwes fi2/2J 0 = 0 186 Sohd circles refer to states wnh a 4p-2h main configuration, squares to 2p states and open circles to states for which the configuration has not been estabhshed.

been identified at 17.6 -+ 0.2 MeV and the 11.69 MeV state has been confirmed to have ,I ~ = 6 +, by measur- ing the d - a angular correlation for the 14C(LI ' da)

reaction at E6LI = 34 MeV. Both these states are populated through &rect a-transfer. These findings and the comparison of the relative a-particle spectros- copic strengths, extracted in the analysis of the angu- lar distribution data taken at the same incident en-

ergy, support the suggestion that this 8 + state is the fifth member of the 4p--2h 180 rotational band based on the 3.63 MeV 0 + level.

This indication well agrees with the plediction of

the folded cluster model [2,3], thus corroborating the existence of a-clustering in light nuclei.

[1] A. Cunsoloetal,Phys Rev. C24 (1981) 476 [2] B Buck, 1I l"rlednch and A A Pill, Nucl. Phys. A290

(1977) 205 [3] B Buck, C B Dover and J.P. Vary. Phys. Rev CI 1 (1975)

1803 [4] A. Cunsolo et al., Nuovo (hmento 40 (1977) 293. [5] E F. da Stlvetra, Proc l-ourteenth Winter Meeting on

Nuclear physics (Bormlo, 1976), unpublished. [6] A Cunsolo et al, Phys Rev C21 (1980) 2345 [7] F I'. da Sllvelra, private commumcatlon.

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